Properties

Label 6.6.1683101.1-13.2-a
Base field 6.6.1683101.1
Weight $[2, 2, 2, 2, 2, 2]$
Level norm $13$
Level $[13,13,w^{2} - 2w - 2]$
Dimension $1$
CM no
Base change no

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Base field 6.6.1683101.1

Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 4x^{4} + 13x^{3} + 7x^{2} - 14x - 7\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2, 2, 2]$
Level: $[13,13,w^{2} - 2w - 2]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $14$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
7 $[7, 7, w]$ $-1$
7 $[7, 7, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + 5]$ $-1$
13 $[13, 13, w^{2} - 3]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}1$
29 $[29, 29, w^{4} - 2w^{3} - 4w^{2} + 4w + 6]$ $-9$
29 $[29, 29, -w^{4} + 2w^{3} + 4w^{2} - 6w - 5]$ $\phantom{-}5$
41 $[41, 41, -w^{2} + 4]$ $-7$
41 $[41, 41, -w^{2} + 2w + 3]$ $-7$
43 $[43, 43, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - w + 3]$ $\phantom{-}5$
43 $[43, 43, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 4w + 2]$ $\phantom{-}12$
64 $[64, 2, -2]$ $-5$
71 $[71, 71, w^{5} - 3w^{4} - w^{3} + 6w^{2} - 2w + 2]$ $-2$
71 $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} - w + 5]$ $\phantom{-}5$
71 $[71, 71, w^{4} - 3w^{3} - 2w^{2} + 6w + 2]$ $-16$
71 $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 19w^{2} - w - 12]$ $\phantom{-}12$
83 $[83, 83, -w^{4} + w^{3} + 5w^{2} - w - 6]$ $-14$
83 $[83, 83, w^{5} - 2w^{4} - 4w^{3} + 6w^{2} + 4w - 1]$ $\phantom{-}0$
97 $[97, 97, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ $\phantom{-}7$
97 $[97, 97, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} + 2w - 2]$ $-14$
113 $[113, 113, -2w^{4} + 3w^{3} + 8w^{2} - 6w - 6]$ $-19$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$13$ $[13,13,w^{2} - 2w - 2]$ $-1$